Ungauged Sites Research Articles

Distributional Regression Forests Approach to Regional Frequency Analysis With Partial Duration Series

AbstractRegional flood frequency analysis (RFFA) is widely used to quantify flood risk at ungauged and sparsely gauged locations. There are minimal attempts to use partial duration series (PDS) for RFFA, though the use of PDS instead of widely used annual maximum series (AMS) can offer some advantages. This article contributes two novel random/regression forests (RFs)‐based methodologies, namely generalized pareto distribution (GPD)‐based distributional RFs (DRFs) and multivariate RFs (MVRFs), for RFFA with PDS. The RFs facilitate modeling interactions between predictors and their complex relationships with the predictands without explicitly specifying them. The DRFs and MVRFs comprise an ensemble of corresponding regression trees, each constructed by recursive binary partitioning of the feature space into meaningful segments. The proposed DRFs account for the sampling uncertainty of PDS in the partitioning and parameter estimation. In DRFs (MVRFs), quantile estimates for an ungauged site are obtained using maximum likelihood estimates (expected values) of GPD parameters corresponding to the segments to which the site belongs. The potential of DRFs and MVRFs relative to two recently proposed techniques (univariate RFs‐based quantile regression, generalized additive model based on GPD) is demonstrated through Monte‐Carlo simulation experiments and a study on 1,031 watersheds in the United States. The key features influencing scale and shape parameters of GPD fitted to PDS of the watersheds are identified as drainage area and 24‐hr rainfall intensity corresponding to 2‐year return period, respectively. Those identified for shape parameter differ from key features known based on analysis with AMS and generalized extreme value distribution.

Predicting Future Ranked Statistics and Recorded Values for Some Statistical Distributions

Regional frequency analysis (AFR) brings together a variety of statistical methods aimed at predicting the behavior of extreme hydrological variables at ungauged sites. Regression techniques, geostatistical methods and classification are among the statistical tools frequently encountered in the literature. Methodologies based on these tools lead to regional models that offer a simple, but very useful description of the relationship between extreme hydrological variables and physiometeorological characteristics of a site. These regional models then make it possible to predict the behavior of variables of interest at places where no hydrological information is available. These methods are generally based on restrictive theoretical assumptions, including linearity and normality. These do not reflect the reality of natural phenomena. The general objectives of this paper are to identify the methods affected by these hypotheses, evaluate their impacts and propose improvements aimed at obtaining more realistic and fairer representations. Projection pursuit regression is a non-parametric method similar to generalized additive models and artificial neural networks that are considered in AFR to take into account the non-linearity of hydrological processes. In a comparative study, this paper shows that regression with revealing directions makes it possible to obtain more parsimonious models while preserving the same predictive power as the other nonparametric methods. Canonical Correlation Analysis (ACC) is used to create neighborhoods within which a model (e.g. multiple regression) is used to predict hydrologic variables at ungagged sites on the other hand, ACC strongly depends on the assumptions of normality and linearity. A new methodology for delineating neighborhoods is proposed in this paper and uses revealing direction regression to predict a reference point representing hydrological and physiometeorological information that is relevant to these groupings. The results show that the new methodology generalizes that of ACC, improves the homogeneity of neighborhoods and leads to better performance. In AFR, kriging techniques on transformed spaces are suggested in order to predict extreme hydrological variables. However, a transformation is required so that the hydrological variables of interest derive approximately from a multidimensional normal distribution. This transformation introduces a bias and leads to suboptimal predictions. Solutions have been proposed, but have not been tested in AFR. This paper proposes the approach of spatial copulas and shows that this approach provides satisfactory solutions to the problems encountered with kriging techniques. Max-stable processes are a theoretical formalization of spatial extremes and correspond to a more faithful representation of hydrological processes on the other hand; their characterization of extreme dependence poses technical problems which slow down their adoption. In this paper, the approximate Bayesian calculus is examined as a solution. The results of a simulation study show that the approximate Bayesian computation is superior to the standard approach of compound likelihood. In addition, this approach is more appropriate in order to take into account specification errors.

Streamflow Estimation at Ungauged Basin using Modified Group Method of Data Handling

Among the foremost frequent and vital tasks for hydrologist is to deliver a high accuracy estimation on the hydrological variable, which is reliable. It is essential for flood risk evaluation project, hydropower development and for developing efficient water resource management. Presently, the approach of the Group Method of Data Handling (GMDH) has been widely applied in the hydrological modelling sector. Yet, comparatively, the same tool is not vastly used for the hydrological estimation at ungauged basins. In this study, a modified GMDH (MGMDH) model was developed to ameliorate the GMDH model performance on estimating hydrological variable at ungauged sites. The MGMDH model consists of four transfer functions that include polynomial, hyperbolic tangent, sigmoid and radial basis for hydrological estimation at ungauged basins; as well as; it incorporates the Principal Component Analysis (PCA) in the GMDH model. The purpose of PCA is to lessen the complexity of the GMDH model; meanwhile, the implementation of four transfer functions is to enhance the estimation performance of the GMDH model. In evaluating the effectiveness of the proposed model, 70 selected basins were adopted from the locations throughout Peninsular Malaysia. A comparative study on the performance was done between the MGMDH and GMDH model as well as with other extensively used models in the area of flood quantile estimation at ungauged basins known as Linear Regression (LR), Nonlinear Regression (NLR) and Artificial Neural Network (ANN). The results acquired demonstrated that the MGMDH model possessed the best estimation with the highest accuracy comparatively among all models tested. Thus, it can be deduced that MGMDH model is a robust and efficient instrument for flood quantiles estimation at ungauged basins.

Simulation of flow at an ungauged river site based on HEC-HMS model for a mountainous river basin

Simulation of flow at an ungauged river site based on HEC-HMS model for a mountainous river basin

Hydroclimatic Data Prediction using a New Ensemble Group Method of Data Handling Coupled with Artificial Bee Colony Algorithm

Linear regression is widely used in flood quantile study that consists of meteorological and physiographical variables. However, linear regression does not capture the complex nonlinear relationship between predictor and target variables. It is rare to find a hydrological application using the group method of data handling (GMDH) model, artificial bee colony (ABC) algorithm, and ensemble technique, precisely predicting ungauged sites. GMDH model is known to be an effective model in complying with a nonlinear relationship. Therefore, in this paper, we enhance the GMDH model by implementing the ABC algorithm to optimize the parameter of partial description GMDH model with some transfer functions, namely polynomial, radial basis, sigmoid and hyperbolic tangent function. Then, ensemble averaging combines the output from those various transfer functions and becomes the new ensemble GMDH model coupled with the ABC algorithm (EGMDH-ABC) model. The results show that this method significantly improves the prediction performance of the GMDH model. The EGMDH-ABC model satisfies the nonlinearity in data to produce a better estimation. Also, it provides more robust, accurate, and efficient results.

Modeling of flood extremes using regional frequency analysis of sites of Khyber Pakhtunkhwa, Pakistan

AbstractThe study provides results of regional frequency analysis (RFA) using annual maximum peak flows (AMPF) of 36 sites located on various streams and rivers of Khyber‐Pakhtunkhwa, Pakistan. Assumptions of randomness, independent and identical distribution regarding AMPF at each site have been validated using different statistical tests. The region of 36 sites is heterogeneous as confirmed by L‐moments based heterogeneity measure. Therefore, it is subdivided into four homogeneous regions considering the most influential site characteristic among available using wards clustering method and Euclidean distance. To identify good‐fit‐regional distribution(s), from a set of popular three‐parameter distributions, L‐moment ratio diagram and |Z‐Dist| statistic are used as goodness‐of‐fit criteria. To obtain the most suitable distribution having robust properties, a simulation‐based assessment analysis is performed for each homogeneous region considering root mean square error and 95% error bounds of regional quantiles as accuracy measures. Due to non‐linearity (in the functional relationship between the mean of AMPF at various sites and their corresponding site characteristics) and the existence of multicollinearity between the site characteristics, radial basis function (RBF) network has been used for the estimation of quantiles at ungauged sites. The results show that the adopted methodology is useful for the estimation of quantiles at gauged and ungauged sites within the defined homogeneous regions.

Regionalización del caudal máximo anual en cuencas del sistema hidrográfico del río Colorado, Argentina

La predicción del caudal máximo anual resulta de utilidad para la gestión de eventos extremos relacionados con crecidas. Para realizar estimaciones con bajo grado de incertidumbre es necesario contar con una gran cantidad de información hidrométrica. Las cuencas que integran el sistema hidrográfico del río Colorado presentan una topografía que dificulta el mantenimiento de las estaciones hidrométricas, razón por la cual, se carece de continuidad en los registros y se presentan en varios casos sectores sin aforar. La regionalización consiste en la transferencia de información de los sitios aforados a los no aforados para la predicción de caudales. El objeto del trabajo fue encontrar la función que relaciona el caudal máximo anual con las características climáticas y morfométricas de las cuencas. Para ello, se emplearon modelos de regresión simple. A partir de dicha relación y la curva de frecuencia regional es posible predecir caudales máximos anuales para diferentes períodos de retorno en cuencas sin aforo pertenecientes al sistema hidrográfico del río Colorado, Argentina. De los doce modelos analizados, los mejores resultados se presentan cuando la variable predictora es el área y perímetro de la cuenca. Los errores de los modelos de regionalización para diversos sitios del sistema resultaron entre el 6% y el 67%. Estos modelos constituyen una herramienta para la gestión de crecidas en el centro oeste argentino.

Frequency analysis of annual maximum rainfall series of fifteen meteorological observatories of Sindh, Pakistan

The study is an application of L-moments based regional frequency analysis using annual maximum rainfall series of fifteen sites of Sindh, Pakistan. Initial screening reveals that the observed data series at each site has no serial correlation and is randomly and identically distributed. The discordancy measure (Di) show that none of the site in a group of fifteen sites is discordant. The regional heterogeneity measure (H) shows that the region of fifteen sites is homogeneous. L-moment ratio diagram and |ZDIST| statistic are in favor of generalized logistic distribution (GLO) as best-fitted regional distribution. Parameters of GLO distribution and regional as well as at-site quantiles for various return periods have been estimated. Results show that the estimated quantiles of each site are greater than the average values of observed data series at corresponding sites. Random forest regression has been used for the estimation of quantiles at ungauged sites.

A Bernoulli-Gamma hierarchical Bayesian model for daily rainfall forecasts

We consider stochastic weather models originally developed for rainfall simulations to build a hierarchical Bayesian mixture model for daily rainfall forecasts using endogenous and external information. We model daily rainfall as a seasonal-varying mixture of a Bernoulli distribution for rainfall occurrence and a gamma distribution for the rainfall amount. The model scheme allows the inclusion of predictors to reduce the bias and variance of the forecasts, while the hierarchical Bayesian framework promotes a better understanding and reduction in parameter uncertainties, especially for gauges with short records, as well as supports the estimation of regional parameters that could be employed for forecasts at ungauged sites. The model was tested using 47 years (1973–2019) of daily rainfall data from 60 gauges in South Korea. Climate indices derived from the low-level wind over the region were analyzed using Principal Component Analysis (PCA) and embodied into the model to enhance its forecast skills. The model structure was based on a detailed exploratory data analysis, which included the application of Self-Organizing Maps (SOM) to examine the spatio-temporal patterns of rainfall. Cross-validated results reveal improved skills over reference models based on climatology and persistence up to a three days lead time. The average gains in metrics such as the Brier and Winkler skill scores vary from 5% to 50%, while the average correlation skill between predictions and observations reach values up to 0.55. The gains beyond a three days lead time are marginal, but the underlying structure of the proposed model still encourages its use over the reference models, being a step forward in improving real-time daily rainfall forecasts for the region. It has also a great potential to be combined with weather model forecasts and applied in other places across the world.

Toward geostatistical unbiased predictions of flow duration curves at ungauged basins

Flow duration curves (FDCs) represent the percentage of time (or duration) during which a given streamflow is equaled or exceeded. Flow duration curves provide a rapid and direct response to the behavior of water resources in a basin. Thus, predicting FDCs is important in basins with little or no monitoring for both all-time and seasonal periods. The geostatistical approach for predicting FDCs at ungauged sites represents an advancement in this research topic. However, poor results have been observed, particularly overestimates (positive bias) for high durations, i.e., low flows. This study aims to predict FDCs in all-time and seasonal periods by using a geostatistical approach based on models, toward unbiased prediction. Streamflow data from 81 stream gauges made available by the Brazilian National Water Agency (ANA) have been used. These stations have a high spatial density and are well spread across the study area. To map the FDCs, and consequently, all their quantiles, the scale and shape parameters of the FDCs were modeled geostatistically. First, some basic assumptions for the FDC parameters such as data normality and spatial stationarity were verified. After an inference by the maximum likelihood method was performed to fit the geostatistical models and estimate the best model forms, we compared them with the benchmark models (i.e. regression models). Finally, the spatial interpolation was performed and the performance was assessed by a leave-one-out cross-validation. The geostatistical models yielded better fits and performance for mapping the FDCs than the regression models. Both the median of relative residuals for all-time and seasonal periods were unbiased for the entire duration. We suggest that the fixed effect modeling of the geostatistical models, associated with external drifts, led to this better and unbiased performance.

Flow Duration Curves from Surface Reflectance in the Near Infrared Band

Flow duration curve (FDC) is a cumulative frequency curve that shows the percent of time a specific discharge has been equaled or exceeded during a particular period of time at a given river location, providing a comprehensive description of the hydrological regime of a catchment. Thus, relying on historical streamflow records, FDCs are typically constrained to gauged and updated ground stations. Earth Observations can support our monitoring capability and be considered as a valuable and additional source for the observation of the Earth’s physical parameters. Here, we investigated the potential of the surface reflectance in the Near Infrared (NIR) band of the MODIS 500 m and eight-day product, in providing reliable FDCs along the Mississippi River. Results highlight the capability of NIR bands to estimate the FDCs, enabling a realistic reconstruction of the flow regimes at different locations. Apart from a few exceptions, the relative Root Mean Square Error, rRMSE, of the discharge value in validation period ranges from 27–58% with higher error experienced for extremely high flows (low duration), mainly due to the limit of the sensor to penetrate the clouds during the flood events. Due to the spatial resolution of the satellite product higher errors are found at the stations where the river is narrow. In general, good performances are obtained for medium flows, encouraging the use of the satellite for the water resources management at ungauged river sites.

A hierarchical Bayesian model of storm surge and total water levels across the Great Lakes shoreline – Lake Ontario

This study presents a novel approach to determine the distribution of compound flood events composed of storm surge and static water levels along the Great Lakes shoreline. A mixture distribution of the bulk (Student-t) and tail (GPD-negative binomial) components of storm surge is estimated in a hierarchical Bayesian modeling framework. Parameters are modeled across the entire shoreline using Gaussian processes and hourly gauged data, with priors for spatial autocorrelation informed by numerical output from a lake hydrodynamic model. The distribution of total water levels is obtained through Monte Carlo sampling that combines the estimated distribution of surge with stochastic traces of static lake levels that account for water level management, seasonality, and plausible variability in water supplies. The approach can therefore support coastal flood risk assessments in cases when the distribution of static water levels changes are due to altered water level management or climate change. The model is applied in a case study on Lake Ontario. Results suggest that spatial variability in parameter estimates varies significantly by month and mixture distribution component. Evaluations of performance indicate the model is able to capture adequately storm surge behavior at gauges across the lakeshore, even under cross-validation. A frequency analysis of total water levels at two ungauged sites is presented, with specific attention given to the implications of model assumptions on uncertainty in design events. The paper concludes with a discussion of model limitations and avenues for future work.

From Standard Weather Stations to Virtual Micro-Meteorological Towers in Ungauged Sites: Modeling Tool for Surface Energy Fluxes, Evapotranspiration, Soil Temperature, and Soil Moisture Estimations

One of the benefits of training a process-based, land surface model is the capacity to use it in ungauged sites as a complement to standard weather stations for predicting energy fluxes, evapotranspiration, and surface and root-zone soil temperature and moisture. In this study, dynamic (i.e., time-evolving) vegetation parameters were derived from remotely sensed Moderate Resolution Imaging Spectroradiometer (MODIS) imagery and coupled with a physics-based land surface model (tin-based Real-time Integrated Basin Simulator (tRIBS)) at four eddy covariance (EC) sites in south-central U.S. to test the predictability of micro-meteorological, soil-related, and energy flux-related variables. One cropland and one grassland EC site in northern Oklahoma, USA, were used to tune the model with respect to energy fluxes, soil temperature, and moisture. Calibrated model parameters, mostly related to the soil, were then transferred to two other EC sites in Oklahoma with similar soil and vegetation types. New dynamic vegetation parameter time series were updated according to MODIS imagery at each site. Overall, the tRIBS model captured both seasonal and diurnal cycles of the energy partitioning and soil temperatures across all four stations, as indicated by the model assessment metrics, although large uncertainties appeared in the prediction of ground heat flux, surface, and root-zone soil moisture at some stations. The transferability of previously calibrated model parameters and the use of MODIS to derive dynamic vegetation parameters enabled rapid yet reasonable predictions. The model was proven to be a convenient complement to standard weather stations particularly for sites where eddy covariance or similar equipment is not available.

ESTIMACIÓN DE CAUDALES EN CUENCAS NO AFORADAS POR EL MODELO HIDROLÓGICO CEQUEAU

El agua es un recurso natural fundamental para la vida en la Tierra y es el componente básico del ciclo hidrológico. La evaluación de la cantidad de agua disponible en una cuenca es un requisito para el desarrollo y administración de los recursos hídricos, ya sea para suministrar agua a la población, agricultura, industria o para la producción de energía. La modelación hidrológica es una de las herramientas principales usadas para estimar caudales en cuencas no aforadas. En este estudio se aplicó el modelo hidrológico distribuido CEQUEAU para estimar los caudales en cuatro sitios no aforados de la cuenca del río Tacotalpa para el periodo de 1965 a 1999. Para la evaluación de la eficiencia del modelo se usaron tres estadísticas: el coeficiente de eficiencia de Nash-Sutcliffe (NSE), el porcentaje de sesgo (PBIAS) y el coeficiente de determinación (R2). De acuerdo con los criterios estadísticos el modelo es muy bueno. CEQUEAU realizó simulaciones con una buena respuesta natural de los escurrimientos de la cuenca.

Impacts of Watershed Physical Properties and Land Use on Baseflow at Regional Scales

Study regionTexas, USA Study focusTexas is a large state in the US that experiences a diversity of climate conditions and water demands. In this study, 130 stream gauging sites and their associated watershed physical and geological properties were used to develop multiple regression models to predict the Baseflow Index (BFI) across Texas. Calculated BFI was derived from daily streamflow data from 1980 to 2017 using the two-parameter recursive digital filtering approach of the Web-based Hydrograph Analysis Tool (WHAT). Three scenarios were developed and validated. The first two scenarios related BFI to topography, climate, and land use. The third scenario used surface geology, soil type and hydrogeology parameters. New hydrological insights for the regionThe models developed showed high performance, low bias, and low relative errors to predict BFI, with R2 values varying from 0.72 to 0.99, and strong agreement with filtered BFI values. The results further showed that there was no specific pattern for BFI variation across Texas ranging from 0.29 to 0.51. Outputs indicated that models developed for scenarios 1 and 3 had higher prediction performance. Additionally, evapotranspiration (ET) contributed to lower model accuracy, since the ET was not categorized as proportional to the percentages of cultivated areas within each basin, but was generalized to represent the whole catchment. The developed models that are reported here can support further research in groundwater modeling and baseflow prediction for ungauged sites that have similar characteristics.

Regional frequency analysis of annual daily rainfall maxima in Skåne, Sweden

AbstractExtreme daily rainfall events are critical for the urban drainage system, human life, agriculture and small catchments. The information about extreme rainfall magnitudes and frequencies is immensely important for civil engineers, city planners, scientists related to water management, rescue operations and flood control works. This study illustrates the results of regional frequency analysis (RFA) of annual maximum daily rainfall (AMDR) of Skåne County, Sweden. L‐moments based heterogeneity measure (H) reveals that the Skåne County is a homogeneous region. Based on the L‐moment ratio diagram and ZDist statistic results, the generalized normal (GNO) distribution is selected as the most suitable regional distribution. The accuracy measures used in K‐fold cross validation indicate that support vector machine (SVM) model is an appropriate model to find the index rainfall at ungauged sites in the region. The sites characteristics, elevation and latitude are identified as the most important variables to explain the variation in mean annual maximum daily rainfall (MAMDR). Finally, spatial maps of predicted MAMDR for different return periods are constructed by using index rainfall combined with regional quantiles. Spatial maps offer an overall view of the expected MAMDR in the region that is helpful for multiple decision makers including infrastructure planners, city planners, emergency managers, engineers and many others.

Fuzzy Ensemble Clustering Approach to Address Regionalization Uncertainties in Flood Frequency Analysis

AbstractVarious regionalization approaches are in use to delineate watersheds in an area into homogeneous groups/regions for regional frequency analysis of hydrologic extremes (floods, droughts). Each approach differs in the underlying assumptions and strategy for regionalization and yields regions that differ in composition. There is ambiguity in the choice of approaches, as none is established to be universally superior in yielding true regions that are unknown. This article proposes a novel fuzzy ensemble clustering (FEC) approach to deal with uncertainty in the composition of regions obtained using different regionalization approaches. It forms fuzzy meta‐regions by integrating information on similarities in watershed groupings found in an ensemble of regions derived using several regionalization approaches. The FEC approach's potential to form effective regions (than those found in the ensemble) and their utility in regional flood frequency analysis to predict flood quantiles at ungauged sites is demonstrated through Monte Carlo simulation experiments and a case study on peninsular India. An ensemble of regions for use with FEC is formed using the region of influence approach, clustering approach based on Gaussian mixture model (GMM), and a hybrid approach which combines canonical correlation analysis with GMM based clustering. The FEC is shown to be effective in grouping similar watersheds even when the ensemble comprises regions having some improperly/wrongly grouped watersheds.

Exponent determination in a poorly gauged basin system in Nigeria based on flow characteristics investigation and regionalization method

In this study, a method for estimating the exponent “n” values of the catchment-area equations of four sub-basins within the poorly gauged Benin-Owena River Basin Development Authority (BORBDA) in Nigeria is presented to enable the estimation of flows at ungauged sites within the basin and the determination of small hydropower (SHP) potential at different locations in each sub-basin and the entire basin. Optimal prediction of streamflow characteristics in poorly gauged basin requires developing a methodology for extrapolation of data from gauged to ungauged sites within the basin. Four sub-catchments of BORBDA, a poorly gauged basin in Nigeria, were investigated using Remote Sensing (RS), Geographic Information System (GIS), statistical techniques, and Natural Resources Conservation Service-Curve Number (NRCS-CN) hydrological model. Discharge values at gauged sites (Qg) were obtained from recorded discharge values collected for 12 months at an established gauging station in each sub-basin. RS and GIS techniques were used to develop classification maps and obtain crucial data like curve number (CN), elevation, Hydrologic Soil Group (HSG), rainfall intensity, slope, area of gauged and ungauged required for evaluating spatial discharge (ungauged) utilizing NRCS-CN model. From the established model for each sub-basin, exponent “n” in the relationship between discharge and catchment area was obtained to be 0.23, 0.41, 0.71, and 0.74. Using the lumped modeling approach, which considers a watershed as a single unit for computation, where watershed parameters and variables were to be averaged produced “n” = 0.52 for BORBDA area, which is within the range of 0.5–0.85 suggested by previous researchers. Obtained BORBDA exponent “n” was validated for use in the entire basin through soil homogeneity test by generating BORBDA soil map which confirms the four sub-basins investigated share similar HSG A, B, and D with BORBDA. The exponent “n” value is useful for predicting flows in ungauged parts of the basin. The exponent “n” value obtained for the basin is helpful in the assessment of discharge and determination of SHP potential at different locations within the poorly gauged BORBDA basin, and the dissemination of the research findings will find practical use and guide to practicing hydrologists in Nigeria and locations around the world with similar challenges of poorly gauged basins particularly Africa and other developing countries.

Design of simulation studies for flood quantile prediction problems at ungauged site

Design of simulation studies for flood quantile prediction problems at ungauged site

Using two-dimensional numerical model for hydrodynamic modelling of a Western Himalayan Alluvial River Reach

This paper assesses the variability and magnitude of flow regimes at ungauged sites of an Alluvial River Reach. A finite element numerical model (TELEMAC 2-D) was used to simulate the river hydrodynamics. The performance of the model is demonstrated by integrating it from January 1, 2001 to January 1, 2016 with a resolution of 0.22° × 0.18° covering the river domain. A sensitivity analysis was carried out to realise the effect of physical parameters along with the mesh resolution on the model output. The model was calibrated and validated using actual field measurements. The statistical results imply that the predictions of water depth and velocity at different sites in the river are in fine agreement with the observed values. Hence, the model succeeded in simulating the river flow for several periods for the reach.